Kiddie Colloquium
Organizers: Andrew Lin & Shengtong Zhang
Upcoming Events
The Riemann integral does not work well with limits, so naturally one wishes to make something better. Thus, every high school or undergraduate math student should attempt to develop a better integral before learning any measure theory. Naturally, they come up with many strange ways to do it,…
Past Events
Ramsey and Turán numbers are both central quantities in graph theory. Both maximize some quantity — the number of edges (Turán) or independence number (Ramsey) — over n-vertex graphs containing no copy of a fixed forbidden subgraph. In this talk, I'll tell you about a quantity that combines the…
I will explain the proof of the following statement: given n vectors in a vector space, let a_k be the number of sets of k of the n vectors which are linearly independent. Then the sequence a_0, a_1, a_2, ... is unimodal. The proof is an application of the Hodge index theorem in algebraic…
An “abstract polyhedron” means, roughly, a graph that “might be the edges and vertices of a polyhedron”. When can we promote “might be” to “is”? This question is answered by a beautiful theorem about circle packings on the sphere. I will explain the proof of this theorem, as well as some…
It turns out you can take the determinant of some linear operators between infinite dimensional spaces (whoa). It turns out the Laplacian on a surface is one of those operators, and the determinant measures something geometric about the underlying space (Whoa!). It turns out that you can…
We will show how to differentiate computer programs (lambda-expressions, Turing machines, etc) by encoding them in a new system called linear logic that endows the space of programs/proofs with the structure of a differential k-algebra. We will discuss this theory from the perspective of the…
This talk plans to design an immersive game for people who are still kids at heart to experience learning mathematics from the very beginning, but in a completely non-traditional way. We will start analysis without \epsilon-\delta, start algebra without writing operators and laws, start topology…
Calculus is hard. In most textbooks and calculus classes, the chain rule (f∘g)′(x) = f′(g(x))∘g′(x) is either not proved, or only partially proved. The reason is that the proof requires knowledge of topology not covered in the first two years of university, and most importantly, the result fails…
Inkscape is a free and open-source vector graphics editor, utilizing the standardized Scalable Vector Graphics (SVG) file format as its main format.
In this talk, we will explore its power in crafting mathematical illustrations. Join us to delve into the fundamentals of Inkscape as…
Given a subset of Euclidean space, we may ask about the space of harmonic functions vanishing on that particular set. In two dimensions, it is easy to see that this space is either trivial or infinite dimensional. Surprisingly, this question becomes drastically different in three dimensions!…
How many lines can one find in high-dimensional space, every pair of which meets at the same angle? How large a multiplicity can the second-largest eigenvalue of a sparse graph have? How can one generate abelian extensions of a real quadratic field? What are the "nicest" generalized measurements…